Mean, Median & Mode (Cambridge (CIE) IGCSE Maths: Extended): Revision Note

Mean, median & mode

What is the mode?

• The mode is the value that appears the most often

  • The mode of 1, 2, 2, 5, 6 is 2

• There can be more than one mode

  • The modes of 1, 2, 2, 5, 5, 6 are 2 and 5

• The mode can also be called the modal value

What is the median?

• The median is the middle value when you put values in size order

  • The median of 4, 2, 3 can be found by

    • ordering the numbers: 2, 3, 4

    • and choosing the middle value, 3

• If you have an even number of values, find the midpoint of the middle two values 

  • The median of 1, 2, 3, 4 is 2.5

    • 2.5 is the midpoint of 2 and 3

  • The midpoint is the sum of the two middle values divided by 2

What is the mean?

• The mean is the sum of the values divided by the number of values

  • The mean of 1, 2, 6 is (1 + 2 + 6) ÷ 3 = 3

• The mean can be fraction or a decimal

  • It may need rounding

  • You do not need to force it to be a whole number

    • You can have a mean of 7.5 people, for example!

How do I know when to use the mode, median or mean?

• The mode, median and mean are different ways to measure an average

• In certain situations it is better to use one average over another

• For example:

  • If the data has extreme values (outliers) like 1, 1, 4, 50
    The mode is 1
    The median is 2.5
    The mean is 14

    • Don't use the mean (it's badly affected by extreme values)

  • If the data has more than one mode 

    • Don't use the mode as it is not clear

  • If the data is non-numerical, like dog, cat, cat, fish

    • You can only use the mode